Question

Select the correct answer. What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1? A. -0.21 B. 0.74 C. 1.35 D. 1.97

Answer 1

Given the:

ln(x + 6) - ln(2x - 1) = 1

Using the logarithm rule:

• ln a - ln b = ln (a/b)

• ln((x + 6) / (2x - 1)) = 1
• ((x + 6) / (2x - 1)) = E ¹

We know,

• e1 = ²'⁷²

• ((x + 6) / (2x - 1)) ≈ 2.72

Simplifying we get,

• (x + 6) = 2.72 (2x - 1)

• x + 6 = 2.72 (2x) - 2.72 (1)

• x + 6 = 5.44x - 2.72

• 8.72 = 4.44x

By cross multiplication we get,

• x = 8.72 / 4.44

• x = 1.97

Therefore, the value of x is 1.97.

The correct option in the exercise ln (x + 6) - ln (2x - 1) = 1 is alternative "D".